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Many computer programs have been developed to calculate the Fast Fourier Transform (FFT). It is the intention of this thesis to develop the tree graph idea, presented by E. 0. Brigham and R. E. Morrow in the article "The fast Fourier transform," into another computer program that will calculate both the forward and inverse Fourier transforms using nonsymmetrical periodic functions. Most of the information obtained was from periodicals with relatively little available in text books. General matrix equations and calculations presented in proofs were developed by this thesis. The tree graph idea was also expanded to a general form. First the matrix equations for the Discrete Fourier Transform (DFT) were developed. Starting with the Fourier transform pair for an aperiodic continuous function and the matrix equations for the DFT, steps were taken to show how these equations were tied together. Two methods for the FFT were evaluated and proven equal to the DFT matrix equations. The more efficient method was written into a computer program which was explained in detail. Finally examples using this computer program were presented. The forward FFT was approximated using input functions such as a rectangular wave, a step function, a sawtooth wave, and a constant. A test for accuracy was also presented using a rectangular wave input time function.

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